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A DECOMPOSITION OF THE CURVATURE TENSOR FIELD ON THE ABBENA-THURSTON MANIFOLD

Park, Joon-Sik

  • Received : 2014.09.23
  • Accepted : 2014.10.29
  • Published : 2014.12.25

Abstract

In this paper, we decompose the curvature tensor (field) on the Abbena-Thurston manifold into three curvature-like tensor fields, and investigate geometric properties.

Keywords

Abbena-Thurston manifold;curvature-like tensor (field);Weyl tensor;Ricci tensor

References

  1. E. Abbena, An example of an almost Kaehler manifold which is not Kaehlerian, Bollettino U.M.I. 3-A (1984), 383-392.
  2. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. I, Wiley-Interscience, New York, 1963.
  3. J.-S. Park and Won Tae Oh, The Abbena-Thurston manifold as a critical point, Canad. Math. Bull. 39(3) (1996), 352-359. https://doi.org/10.4153/CMB-1996-042-3
  4. J.-S. Park, Curvatures on SU(3)=T (k; l), Kyushu J. Math. 67 (2013), 55-65. https://doi.org/10.2206/kyushujm.67.55

Acknowledgement

Supported by : Busan University of Foreign Studies